A storage tank of negligible mass and 30m high is filled with gasoline. Please calculate the following. Use density values found in the book.
a) The gauge pressure and absolute pressure at the bottom of the tank.
b) The force that acts on a square access hatch at the bottom of the tank that measures 0.5m x 0.5m.
c) Given that the tank is shaped like a right circular cylinder with a height of 30 m and with a
base radius of 10m. The tank is attached to a
steel cable of negligible mass and immersed in water. Calculate the tension (force) in the cable before and after it is immersed in water.
All I am needing help on is the equations. Once I have the equation I can get the answers myself thank you!!
gage pressure = density * g * height
absolute pressure = gage pressure + 1 atm (about 10^5 N/m^2 or Pascls)
Force = gage pressure * area
(use gage pressure because we assume one atm is pushing up from underneath)
tank volume = pi r^2 h
weight of gas = gas density * volume * g
(tis is the tension in the lifting cable with tank in air)
weight of water outside = buoyant force up = water density * (VOLUME) * g
Note about VOLUME of water displaced.
This tank will FLOAT because gasoline is less dense than water. There will be no tension in the cable unless the cable pulls the tank down.
Sure! I can help you with the equations for each of these calculations.
a) The gauge pressure at the bottom of the tank can be calculated using the equation:
P = ρgh
Where:
P is the pressure (in Pascals),
ρ is the density of the gasoline (in kg/m^3),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and h is the height of the fluid (30m in this case).
The absolute pressure at the bottom of the tank can be calculated by adding the atmospheric pressure to the gauge pressure.
b) The force acting on the square access hatch at the bottom of the tank can be calculated using the equation:
F = P * A
Where:
F is the force (in Newtons),
P is the pressure (in Pascals, which can be calculated using the previous equation),
and A is the area of the square hatch (0.5m x 0.5m = 0.25 m^2 in this case).
c) The tension in the steel cable can be calculated using the equation:
T = mg + F_buoyant
Before the tank is immersed in water, there is no buoyant force, so the equation simplifies to:
T = mg
After the tank is immersed in water, the buoyant force can be calculated using the equation:
F_buoyant = ρ_w * V_displaced * g
Where:
ρ_w is the density of water (in kg/m^3),
V_displaced is the volume of water displaced by the tank (which can be calculated using the formula for the volume of a cylinder),
and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Sure! I can help you with the equations for each part of the question.
a) To calculate the gauge pressure and absolute pressure at the bottom of the tank, you can use the equation for pressure:
P = ρgh
Where:
P is the pressure,
ρ is the density of the gasoline,
g is the acceleration due to gravity, and
h is the height of the column of gasoline above the bottom.
For gauge pressure, you need to subtract atmospheric pressure from the absolute pressure. Atmospheric pressure is usually around 101,325 Pascal (Pa).
b) To calculate the force that acts on the access hatch at the bottom of the tank, you can use the equation for force:
F = P * A
Where:
F is the force,
P is the pressure at the bottom of the tank (which you calculated in part a),
A is the area of the hatch.
c) To calculate the tension (force) in the cable before and after it is immersed in water, you need to consider the weight of the tank and gasoline. You can find the weight by multiplying the mass by the acceleration due to gravity:
Weight = m * g
Where:
m is the mass of the tank and gasoline,
g is the acceleration due to gravity.
The tension in the cable before it is immersed in water is equal to the weight of the tank and gasoline. After immersion in water, the buoyant force needs to be considered. The buoyant force is equal to the weight of the water displaced by the tank.
I hope this helps! Let me know if you have any further questions.